


An illustrated periodic table of hadrons

by Charles_Rockafellor



Category: Meta - Fandom
Genre: Baryons, Hadrons, Mesons, QCD, particle physics, periodic table, walkthrough
Language: English
Status: Completed
Published: 2021-02-21
Updated: 2021-02-21
Packaged: 2021-03-12 15:54:57
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 3,092
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/29512119
Author URL: https://archiveofourown.org/users/Charles_Rockafellor/pseuds/Charles_Rockafellor
Summary: If you're building a hardcore sci-fi world, then it helps to know real world particles and how they relate to one another, so here's a quickprimerwalkthrough. Normally, the quarks, gluons, leptons, and gauge bosons are presented only slightly arranged, without any great overview of hadrons (these usually being left to tables of data without structure); here we look at hadrons (both the mesons and the baryons) arranged in a periodic array (essentially three dimensional [within the constraints of a 2D screen plus perceived Z-depth], though technically some cells having multiple contents could be construed as spin-like further dimensions).Why?Because this will provide you a starting point for plausible particle decays, a working knowledge of at least which particle relates to another in some way (quark content, charge, etc.). Adlibyons and ergogenic fields (just my own names) are no problem inpulpsci-fi (which I love), but not so great if you're ficcing on something from Forward, Benford, Egan, Metzger, or Cramer. If you can't tell the difference between a proton and a delta, then this is a good spot to start from.𝑫𝒐𝒏'𝒕 𝒇𝒐𝒓𝒈𝒆𝒕 𝒕𝒐 𝑳𝒊𝒌𝒆, 𝑺𝒉𝒂𝒓𝒆, 𝒂𝒏𝒅 𝑺𝒖𝒃𝒔𝒄𝒓𝒊𝒃𝒆! ❤️
Kudos: 1
Collections: Worldbuilding Meta





	An illustrated periodic table of hadrons

**Author's Note:**

> If you like this one, then you'll probably enjoy the next one even more: an extrapolation of **[GEN 0 hadrons](https://archiveofourown.org/works/29688639)** (covering masses, nuclei and chemistry, terrestrial conditions, stellar fusion [touching on quark stars' equations of state], solar evolution, and element distribution [w.r.t. the philosophical implications to any intelligent life in such a world]). Just think of what your mad scientists and basement tinkers might do with this in your next story. 
> 
> Why? Because it was part (a _tiny_ part) of a flashback that Sonic (the Hedgehog) had in [one of my fics](https://archiveofourown.org/works/24230851/chapters/58380841), and I thought that I'd share it as a walkthrough of how one might apply this (or you could just lift the bits that you like for your own fic and not worry about how I arrived at the results). It's sufficiently different that I couldn't really justify making it a second chapter to this piece, so if that's not really your thing, then you might want to skip straight to the fourth installment in the series: [Categorical Logic](https://archiveofourown.org/works/29874783). (“How in the world does _that_ play into fanfics?” you ask? Go see. 😉 I managed something like it for [a Jules Verne & H. G. Wells fic](https://archiveofourown.org/works/27330745) [involving my own modification of the Janet left-step periodic table], and rumor has it that Sherlock Holmes has seen some regained popularity in the past decade.)

  
**Contents:**  
[Intro]  
Mesons and baryons  
Hadrons all in one, plus charge  
Naïve mapping of antibaryons  
Adjusted antibaryon map  
Plain symbol array  
Closing  


####  Background 

The “hadron octahedron” that Tails quizzed Peach about in the epilogue of “I am Legion” (see _[Chapter 6: Back to Kansas](https://archiveofourown.org/works/24354049/chapters/58732195)_ ) is a bit of a misnomer, since although it forms a simple octahedral array in DIM 3, some of the cells contain two or three entries (and one has six), but it fits for now. It's not been published by anyone else that I know of, though there are a couple of schema that arrange hadrons one way or another, and the [Stowe periodic table](https://www.google.com/search?q=Stowe+periodic+table%20-scerri) of the chemical elements shocked the hell out of me [[Stowe-Janet-Scerri](https://www.google.com/search?=&q=Stowe-Janet-Scerri) less so] in its similarity when I first ran into it five or ten years ago (though with great relief, I soon clicked in and found that it wasn't about hadrons, nor extended to them).

It started out in a physics forum in 1998-1999. I'd been in a somewhat frustrating thread and had been beginning to wonder – in print – if one of the other members weren't a 'bot, due to some of the replies' indirect and ambiguously bland nature; the not-actually-a-'bot was similarly frustrated with me (and possibly others), and posed a particle decay question. I don't remember now what that question was, but it was a simple one, something like asking what a Σc+ (i.e.: udc, I = 1, J _P_ = 1/2) would [typically] decay into. Without even thinking of working it out by decay equations (I had _no_ clue how to), I figured that it should be a fairly quick look-up (after all, VNR CRC [or maybe van Nostrand's?] used to have some wonderfully meticulous charts of decay fractions, and I'd spent hours poring over them in the mid-'80s), only to find nothing. At least a brute force approach should have been a simple narrowing-down of possibilities: exclude hadrons that are too heavy, exclude CPT violations, etc., and have a small set of results (hopefully with percentage chances).

I researched that night or the next day (work schedule) and worked out two possibilities, and was pissed off upon finding that he'd posted the answer within 24 hours (when the thread had so far been the usual: maybe one or two replies during the mornings and afternoons, and a flurry of them in the evenings). I don't remember if I actually got the answer right or not, though I feel a vague memory of getting not-quite-right yet close enough that he was pleased with it (read as: I had done far better than he'd expected, and would presumably have gotten a cookie for it).

That incident got me wondering though: baryons and mesons are seen as composite particles, so why wasn't there a simple combinatorial chart for them already? We had one for simple unitary proton progression (periodic table), and there were similar things for nuclides (binary matrix of proton and neutron progressions). So I built one of my own, and sat on it since then. I never submitted it to any physics journals (underachiever or realistic?), nor self-published it anywhere else (academic suicide), so what you're seeing is unvetted, but at least you get the experience of being among the few who've yet seen it.

Initially it was a bit ugly, with the baryon combinations structured tetrahedrally. Functional, sure, but when you color coded isospin, or electrical charge, etc., it was a mess; blatantly non-symmetric. Below you see an approximate reconstruction of the original arrangement (the exact sets might have been arranged differently, but the essential structure is the same). Note that hadrons are just like a bag of groceries: it's a combination of whatever's inside, not a permutation of what went in first, so 123 = 132 = 231.

Why include it here? Because while I'd love to present a complete work in a professional setting, it would feel disingenuous to me if I were to do so here – I'd rather show the whole process, to include missteps.

  
**_[open image in new tab](https://i.pinimg.com/originals/10/f6/51/10f651284ddd5a94c368841f79c1ff9a.png) to zoom_**

####  Mesons and baryons **Contents ↑**

That wasn't the case with the mesons – they were nicely ordered. (I don't remember if I'd run into this matrix online before that or not, though I'm almost certain that I have since then.) They're arranged here by increasing mass, rather than purely alternating charge (I grant that it's _prettier_ the other way around, with a nice sequence of alternating {0, +, ...} and {-, 0, ...} rows [or alternating {0, -, ...} and {+, 0, ...} _columns_ , if you prefer], but sequencing them by increasing mass _feels_ more sensible to me).

Depending on how much you already know, you might wonder why the mesons are pairs and the baryons were triplets, or why some of the quarks have overbars and some don't. That's because baryons are bags of three quarks (and antibaryons bags of three antiquarks, and so would all have overbars in the contents), whereas mesons are pairs of one quark and one antiquark. There are exotic mixes (whether actually observed or purely hypothetical) with other content combinations, but we're not going to go that far here.

  
**_[open image in new tab](https://i.pinimg.com/originals/a6/62/66/a66266cc4c736131d1cc3cfc1216100d.png) to zoom_**

I struck upon the idea of simply giving each of the three generations a dipolar axis of their own (far more easily arrayed in two dimensions than trying to represent six independent scalars from a shared origin), to form an octahedral space. It all fell together beautifully, including the charges' color coding, and even the eightfold way multiplets sprang forth naturally from the whole. That's what you see in the next spreadsheet excerpt below. The color coding present is only to highlight those cells with multidimensionality.

Understand that this is entirely my own arrangement, not a standard one, nor one that I've seen anyone else put together.

  
**_[open image in new tab](https://i.pinimg.com/originals/6a/5f/f2/6a5ff26b2f343c62194b50ccf2fc8016.png) to zoom_**

You'll note that even as is, this array requires DIM 3 in general, but needs 2 or 3 more dimensions for those cells that contain multiple entries (none have much claim to the coordinates, though some argument could be made for those that are at least in line with their respective axis, e.g.: btt more so than udt or sct). This is without yet accounting for isospin (e.g.: uds Λ vs. uds Σ).

####  Hadrons all in one, plus charge **Contents ↑**

So I looked at it, smugly satisfied with myself, and wondered if I couldn't work the mesons into the gaps between the baryons. Maybe it would make more sense in one way, while losing some sense in another way, but I threw them together to see how it would look. That's what you have below, showing all of the hadrons in a single combinatorial array (color-coded highlighting **1** by electrical charge: red = 2++, yellow = 1+, green = 00, blue = 1-).

  
**_[open image in new tab](https://i.pinimg.com/originals/c2/7e/ed/c27eed6a8617cf7337a32d80b67b8683.png) to zoom_**

Ahh, so much prettier, hmm? Oh, wait now... <sigh>. We have mesons mixing very nicely with baryons, but that introduces an imbalance: either we consider only some of the mesons to **be** mesons and the others to be antimesons (even though they're all simply one quark and one antiquark, giving them footing in each domain and no a priori reason to call them either at all per se)... or we remove them or add antibaryons.

I'm not fond of any of these options, but let's see where they lead.

  1. Remove _which_ mesons for being antimesons, precisely? (Not that this is a pressing question, since I'm not in charge of particle naming conventions.)  
Presumably those defined as being antimesons (and the convention of naming meson vs. antimeson [isn't entirely straightforward](https://www.osti.gov/servlets/purl/5545302)), but what would we do with those that are their own antimesons?  
Well, maybe we **won't remove** them (which would have left the combinatoric arrangement imbalanced anyway), but let's at least see what it would look like (see **_next_** illustration).  
This is a serious question though: since everyday-matter baryons are thought of as qqq and antimatter antibaryons as q̅q̅q̅, the classic pulp sci-fi go-to dichotomy of matter / antimatter isn't quite so clear cut when considering a hypothetical stable material composed of qq̅, where should mesons fall in a realistic sense? For practical physics, it might not much matter, but for sci-fi – esp. hardcore – it's a bit of a nuisance (and not being in charge of naming conventions, I can't simply invent my own terms in hardcore sci-fi). 
  2. Remove _all_ of the mesons?  
We already know that one from the original baryon octahedron. It might make sense to remove them all for a couple of reasons, but we **_needn't duplicate_** the illustration. 
  3. Add antibaryons?  
It adds an extra dimension to each qqq, but... sure, we'll **try that too** (see illustration **_after_** next). 



  
**_[open image in new tab](https://i.pinimg.com/originals/05/82/56/058256739bebf28df1223f402da60d76.png) to zoom_**

Above is example 1, the removal of only the antimesons (top-flavored mesons assumed IAW positive mesons being material and negatives being antimaterial) would leave yawning gaps that wouldn't be terribly symmetrical, but still viable I suppose.

####  Naïve mapping of antibaryons **Contents ↑**

Let's try that again below with example 3 instead: the addition of antibaryons. It gives the complete set of qqq, q̅q̅q̅, and qq̅ combinations all in a single array; whether the result adds any value is an open question.

  
**_[open image in new tab](https://i.pinimg.com/originals/a0/00/91/a00091dd28446a6155c2ee4269e120d9.png) to zoom_**

A bit dense, but functional.

One small problem though: all that we did was swap the anti-triplets into their counterparts' cells. Sounds sensible enough, but the electrical charges don't equate: uuu might be the complementary coordinate equivalent of d̅d̅d̅, but electrically uuu = ++ and d̅d̅d̅= +.

####  Adjusted antibaryon map **Contents ↑**

Let's see how the antibaryons look all by themselves (this time with a slightly different color-coding due to different resulting electrical charges: yellow = 1+, green = 00, blue = 1-, lavender = 2-):

  
**_[open image in new tab](https://i.pinimg.com/originals/be/dd/6a/bedd6a562d3b851404bad025ad570051.png) to zoom_**

That paints a very different picture indeed. Combining the now-correctly-placed antibaryons into the extant arrangement results in a mess, but at least as separate arrays you can see how the quark contents relate to one another. 

How well do they all get along if we go from simple combinatorial sets to actual identified-by-name particles? Hmm... not so simple. In chemical elements, we don't worry about a zillion different cases of excitation states, so the table is easy (even if we [expand it for nuclides](https://en.wikipedia.org/wiki/Table_of_nuclides)) – i.e.: with nuclides, their excited states are well-identified as being the same damned element. Not so for hadrons, as shown with mesons below (tensors J _P_ 2+ and [J _P_ 2-?] pseudotensors not included for brevity, **top-flavored hypotheticals in red** IAW [2016 PDG naming conventions](http://pdg.lbl.gov/2016/reviews/rpp2016-rev-naming-scheme-hadrons.pdf) for reference [[2018 available here](http://pdg.lbl.gov/2018/reviews/rpp2018-rev-naming-scheme-hadrons.pdf)] and [2020 here](https://pdg.lbl.gov/2020/reviews/rpp2020-rev-naming-scheme-hadrons.pdf)) – i.e.: subatomic particles aren't nearly so paparazzi-friendly (hence their identifications sometimes being somewhat tentative); that doesn't actually explain the ridiculous explosion of names for the different excited states of a given particle, which is simply a case of ~~laziness~~ <*ahem*> _physicists wishing to keep established names as-is_ (in order... to minimize... confusion).

  
**_[open image in new tab](https://i.pinimg.com/originals/11/06/17/11061706d915e1f025d10b33ccc85d9d.png) to zoom_**

Excluding the excited states so that we focused solely upon pseudoscalars would simplify matters:

  
**_[open image in new tab](https://i.pinimg.com/originals/5a/ca/92/5aca9213817095cbe5564d8a6e76e50d.png) to zoom_**

...though this would then lead to a similar result for baryons (e.g.: exclude J _P_ 3/2 Δ in favor of J _P_ 1/2 N). Multiple tables for multiple states would satisfy this without losing the other states' representation, but would obviously mean multiple tables (should it then extend further to 5/2, 7/2, 9/2, … ?).

See also: Particle Data Group's [2018 rev. quark model](http://pdg.lbl.gov/2018/reviews/rpp2018-rev-quark-model.pdf) & [2020 update](https://pdg.lbl.gov/2020/reviews/rpp2020-rev-quark-model.pdf).

####  Plain symbol array **Contents ↑**

Where does all of this leave us? Nowhere very useful without knowing which particles these quark contents are, so here's the hadron octahedron with the symbols put in place of the quark contents:

  
**_[open image in new tab](https://i.pinimg.com/originals/0c/cb/07/0ccb076bc5311fd8ecf75b1c55481f83.png) to zoom_**

####  Closing **Contents ↑**

What about decay paths (there's a lot of mention of these in some sci-fi)?

That's a mouthful. Quarks will decay to lighter flavors, but the paths are probabilistic. Their half-lives, which particular hadron is more likely than the other possibilities... all that you can nail down is that the results will be lighter (same number of quarks, but of lower mass each, and with less binding energy between them, but in a higher ratio to the sum of the reduced quark masses: for a quick estimate, subtract the quarks' masses from a particle's mass, and you have the total binding energy), and usually in only one or two biggish pieces per decay instead of a bunch of littler ones all at once. That is: you might figure that (for example) a Σb+ (uub) is more likely to decay [directly] into an Ωcc+ (scc) plus other things than into some other baryon, and it makes sense since that's a lighter particle than you started with, but it's [not a simple sequence by mass](https://en.wikipedia.org/wiki/Weak_interaction#Properties) (click that link to see how and why): that b might decay to a c more likely than to a u, but not [directly] to an s or a d – though you'd be right in assuming that the baryon isn't about to decay into anything heavier at all (barring vacuum fluctuations), so you can at least say that the Ωcc+ is a step in the right direction. You can also rule out the possibility of it decaying directly into a horde of nucleons and pions (this might be its eventual fate, but not without intermediate decays).

The decays also involve other products: photons, neutrinos, etc..

Then there's the summing over of all of the possible paths. An infinite set of terms.

Way too much there to even scratch at here (and way heavier than I can even pretend to follow), so I'll just point you to the [Feynman](https://www.youtube.com/results?search_query=Feynman+lecture) and [Susskind](https://www.youtube.com/results?search_query=Susskind+lecture) lectures, and [Khan Academy](https://www.khanacademy.org/science/physics/quantum-physics/in-in-nuclei/v/alpha-beta-and-gamma-decay) instead.

What you've seen here is all only a set of conceptual scaffolds, ignoring the mixing of eigenstates, and none of them name the qqq (or q̅q̅q̅) and qq̅ sets in a convenient whole (just sets of each that you can compare, or a couple of scattered particular cases in the main text), or break them down by isospin (e.g.: uds; Λ _I_ = _0_ , Σ _I_ = _1_ ) or angular momentum configurations (e.g.: N {uud, udd}, J _P_ = 1/2; Δ {uuu, uud, udd, ddd}, J _P_ = 3/2) – or at least differentiate between those that have been observed and those that haven't, and those that can't – but the set in general at least gives you the gist of things.

Maybe it would be better arranged in DIM 12, to account for each quark and antiquark as its own axis, and each particle could then be a hypercubic coordinate (other excitation issues aside), and this would at least allow for certain hypothetical structures such as tetraquarks, but DIM 12 isn't visually intuitive for DIM 3 eyesight and DIM 2 displays, nor would that particular example incorporate other exotica such as gluonium [“glueball”] states. All of this would still be without really addressing flavor-spin complications of extending SU(6) to six flavors and two spins as SU(12).

Ignoring the t quarks might simplify the resulting array, but would also remove a degree of symmetry that seems inherent to the nature of things (even if t quarks decay too quickly to bond with others).

There are a lot of important points that I didn't go into, or touched on only briefly (more likely tangentially). The isn't the place for those (since I'm only trying to give a foundation to work with for those interested in giving their sci-fi a more realistic bent), and I'm not qualified to do so.

Those who are familiar will already have noticed the stuff that I've skipped (and yes, I acknowledge that I played pretty fast and loose with color content, mixed states, K0S/L or η/η′, |uu̅-dd̅〉/√2 [and other such], isospin 3/2 as a ground state, higher resonances, strangeness, etc. – though to be fair, strangeness is a bit pointless). Those who've gone far with it will probably be cringing at egregious errors that I've made unwittingly, or the imprecise language that I've used to convey things.

For everyone else who's just trying to grok it at all, I hope that I've kept it in plain English enough to get you started or give you a better handle than blind tables of numbers. It's hard to ask the right questions when you don't even know the words needed. Aside from that, the other goal is the usual lesson: just as with writing fanfic for stories that _you_ want to read (maybe a John W. Campbell fanfic, or E. E. “Doc” Smith, or A. E. van Vogt, plus a dash of current particle data?), if it doesn't exist (like say, a periodic table of hadrons?), then go research and make one for yourself. (Now go let your geek-flag fly!)

But as for further research, if you're inclined to go a bit further into it... honestly, my suggestion is to hit Wikipedia as a starting point (it's not great, but it'll do), then spin by [Hyperphysics](http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/parcon.html), and finally dive back into [PDG](https://pdg.lbl.gov/2020/listings/contents_listings.html):

  * [hadrons](https://en.wikipedia.org/wiki/Hadron)
  * [mesons](https://en.wikipedia.org/wiki/Meson)
  * [meson list](https://en.wikipedia.org/wiki/List_of_mesons)
  * [baryons](https://en.wikipedia.org/wiki/Baryon)
  * [baryon list](https://en.wikipedia.org/wiki/List_of_baryons)



If you enjoy this stuff, but it's a bit too heavy, then I recommend “ _Black Holes and Time Warps_ ” (Kip S. Thorne, 1994) and “ _The Anthropic Cosmological Principle_ ” (Barrow & Tipler, 1986); the latter is primarily philosophical for the first third (or 2/3?), but gets to the physics in good time. There are also some really interesting (old) pieces from Scientific American, “ _Particles and Forces: At the Heart of Matter_ ” (1990) and “ _Particle Physics in the Cosmos_ ” (1989), which go for about $25 each on Amazon, these days: though I imagine that there's more-up-to-date material out there by now, I can say that they're definitely an excellent set to begin branching out if you're thinking of looking into richer, broader material.

If this material is too light and fluffy for your level, then I recommend [arXiv](https://arxiv.org/). Really good material there, some of it being fairly standard and some rather bleeding edge. You won't be disappointed (though sometimes you'll need your Google Fu in order to find the more rare items elsewhere).

You might also consider [viXra](http://vixra.org/); it has a bit of disrepute to it, but that doesn't necessarily make a given paper wrong – and regardless of veracity or lack thereof, that doesn't necessarily mean that something isn't an interesting read, or might not spark a perfectly valid line of reasoning (or maybe... game / fiction ideas?).

**O ~~~ O**

**Author's Note:**

>  **1** For those who'd like to be able to colorize their fonts, highlight things, change from one font to another (e.g.: AO3's Verdana family default to something like Times New Roman), change font sizes, etc., here's my tutorial as a starting point: “[Fonts, and colors, and work skins, oh my!](https://archiveofourown.org/works/28934610)”. 🙂


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